Multi-trace correlators from permutations as moduli space

We study the n-point functions of scalar multi-trace operators in the U(N-c) gauge theory with adjacent scalars, such as N = 4 super Yang-Mills, at tree-level by using finite group methods. We derive a set of formulae of the general n-point functions, valid for general n and to all orders of 1/N-c. In one formula, the sum over Feynman graphs becomes a topological partition function on Sigma(0,n) with a discrete gauge group, which resembles closed string interactions. In another formula, a new skeleton reduction of Feynman graphs generates connected ribbon graphs, which resembles open string interaction. We define the moduli space M-g,n(gauge) from the space of skeleton-reduced graphs in the connected n-point function of gauge theory. This moduli space is a proper subset of M-g,M-n stratified by the genus, and its top component gives a simple triangulation of Sigma(g,n).